Area of triangles and parallelograms: [Short Answer Questions] Important Questions for SLC Examination

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1 # Section I a) Find the area of the triangle given below. Area of triangles and parallelograms: [Short Answer Questions] Important Questions for SLC Examination b) Find the area of an equilateral triangle whose side is 6cm. c) The area of equilateral triangle is 4 3 cm 2, find the perimeter. d) The perimeter of equilateral triangle is 24cm, find it's area. e) In the given rhombus, PQ = 6cm and PT = 4cm, find the area of the rhombus PQRS. f) In the adjoining figure, PQRS is a rhombus. If PR = 4cm and QS = 6cm, find the area of PQRS. g) In the adjoining figure, ABCD is a rhombus. If the area of ABCD = 36cm 2 and the diagonal AC = 8cm, find the length of the diagonal BD. h) Each side of rhombus measures 10cm, diagonal is 12cm long, find the length of other diagonal. i) Find the perimeter of a rhombus ABCD whose diagonals AC and BD are 12cm and 16cm respectively. j) Find the area of square ABCD in which diagonal BD = 3 2 cm. # Section II a) Calculate the area of the given quadrilateral in which CX = 6cm, AY = 8cm and BD = 8cm. b) PQRS is a quadrilateral in which PR = 10cm, perpendiculars from S and Q on PR are 3.4cm and 4.6 cm respectively. Calculate the area of the quadrilateral. c) Find the area of the given quadrilateral ABCD where AM and CN are perpendiculars to BD and 4AM = 2CN = BD = 12cm. d) Find the area of the given quadrilateral PQRS where PA and RB are perpenducular to QS and 3RB = 2PA = QS = 6cm. Page 1 of 5

2 e) In a quadrilateral ABCD, diagonal AC = 17cm, perpendiculars from B and D on AC are 11cm and 9cm respectively. Calculate the area of the quadrilateral. f) The diagonals of rhombus are 10cm and 12 cm respectively. Find it's area. g) If the area of rhombus is 90 3 cm 2 and its one diagonal is 30 3 cm. Find its other diagonal. # Section III a) In the given figure, ABCD is a parallelogram, ADP = 7cm 2 and BCP = 5cm 2, find the area of parallelorgram ABCD. b) M is the midpoint of the LN of KLN. If the area of KLN is 30cm 2, what will be the area of KMN? c) ABCD is a square and EBCF is a parallelogram. If AB = 4cm, calculate the area of the parallelogram EBCF. d) If parm ABCD, BC = 2QC and P is any point on AD If area of parm ABCD is 48cm 2, find the area of PQC. # Section IV a) In the given trapezium PQRS, PQTS is a rectangle. If PS = 8cm, QR = 11cm and SR = 5cm, find the area of trapezium PQRS. b) Calculate the area of the given trapezium ABCD. c) In the given figure AB//FC, AB = 18cm, FC = 28 cm, EC = 23cm, AF = 13cm & AE FC. Find the area of the figure ABCF. d) In the given figure AB//DC, AB = 10cm, DC = 14 cm, AD = 5cm & AE DC. Find the area of trapezium ABCD. e) The given figure is a trapezium ABCD in which AB//DC and BCD = 90 0, if CD = 7cm, AB = 17cm and AD = 26cm, calculate the area of the trapezium ABCD. f) The given figure is a trapezium PQRS in which PQ//SR and PQR = 90 0, If PQ = 10cm, SR = 18cm and PS = 17cm, calculate the area of the trapezium PQRS. Page 2 of 5

3 g) In a given ABC, if X and Y be the mid-point of AB and AC respectively & XM BC. Find the area of BXYC. # Section V a) The areas of two parallelograms are equal and their altitudes are 6cm and 9cm. If the base of the first parallelogram is 12cm, find the base of the second parallelogram. b) The area of two parallelograms are equal. The altitude of one parallelogram is 4cm and the base of the other is 6cm. If the base of the first parallelogram is 9cm, find the height of the second parallelogram. c) ABCD is a trapezium with area 60sq.cm. where AD//BC, AF BC. If BC = 10cm and AF = 8cm, find the value of AD. d) The parallel sides of a trapezium are 4.3 cm and 5.7 cm If its area is 40sq.cm, find its height. e) ABCD is a trapezium in which AB//CD, AD = BC = 13cm, AB = 18cm and DC = 28cm, Find the area. f) Two adjacent sides of a parallelogram are 12 and 30 units and they include an angle of Find the area of the parallelogram. # Section VI a) Find the area of a parallelogram whose base is (x + 2) and altitude is (2x -4) b) If the sides of parallelogram are doubled, how does the area of the parallelogram The area of parallelogram is 2x 2 + 3x - 9 square units and the base is (2x - 3) units. Find the length of the altitude drawn to the base. d) A parallelogram MNOP, M = 45 0, altitude PR = 5cm and diagonal PN = 13cm, Find the area of the parallelogram e) Find the altitude of an equilateral triangle whose area is 36 3 cm 2 f) Find the area of an equilateral triangle whose altitude is 4 3 units. g) Find the area of an isosceles right angled triangle whose hypoteneous is 8 cm. h) The sides of an equilateral triangle is 8cm, Find the length of other equilateral triangle, with twice the area. # Section VII a) In the given figure, parallelogram PQRD and EQR are on the same base and between the same parallel. If the area of the EQR is 7 square cm, find the area of the parallelogram PQRD. b) In the given figure, ABCD is a square and EBC a triangle. If AB = 6cm, calculate the area of the triangle EBC. c) In given parallelogram ABCD, AM BC, AN CD BC = 15cm, AM = 8cm and AN = 10cm, find the perimeter of the parallelogram. d) In the parallelogram ABCD, BC = 12cm, DC = 10cm and area of parallelogram = 96 sq.cm. Calculate the lengths of altitude AM and altitude AN. # Section VIII a) In the given figure, PORS is a parallelogram in which T is the middle point of PS. If the area of the PTO is 6cm 2, what will be the area of the quadrilateral OTSR. Page 3 of 5

4 b) In the given figure, BOY is triangle. in which M and N are the mid-points of OY and OM respectively if the area of BOY = 30cm 2. Find the area of MBN. c) In the given figure, BD = DC = 2BE and ABE = 12cm 2, find the area of ABC. d) In the given figure, QR = RS and PM = RM. If MQR = 6.5 cm 2, find the area of PQS. e) In ABD, ED = 2AE, BC = CD and ABD = 64.8cm 2 find the area of BEC. e) Find the area of PQR from the given figure. # Section IX a) In the given figure MN//PR, Prove that MOP = RON. b) In the given figure, M is the midpoint of the diagonal BD of quadrilateral ABCD, then prove that area of quadrilateral AMCD and quadrilateral AMCB are equal. c) In ABC, P is any point on median AD then prove that APB = APC. # Section X a) The area of rhombus is equal to one half the product of its diagonal prove b) Prove that area of a kite is equal to one half the product of diagonals. c) Prove that area of trapezoid is half of the products of its altitude and sum of the bases. d) Prove that the area of a quadrilateral is equal to one half the product of a diagonal and the sum of perpendiculars on it's from the opposite vertices. e) Prove that median of triangles divide the triangle into two triangles of equal area. Page 4 of 5

5 Answers I. a) 126cm 2 b) 9 3 cm 2 c) 12cm d) 16 3 cm 2 e) 24cm 2 f) 12cm 2 g) 9cm h) 16cm i) 40cm j) 9cm 2 II. a) 56cm 2 b) 40cm 2 c) 54cm 2 d) 15cm 2 e) 170cm 2 f) 60cm 2 g) 6cm III. a) 24cm 2 b) 15cm 2 c) 16cm 2 d) 12cm 2 IV. a) 38cm 2 b) 48cm 2 c) 276cm 2 d) 36cm 2 e) 288cm 2 f) 210cm 2 g) 45cm 2 V. a) 8cm b) 6cm c) 5cm d) 8cm e) 276cm 2 f) 180 sq. units VI. a) (2x 2-8)sq. units b) 3 times c) (x + 3)units d) 85cm 2 e) 6 3 cm f) 16 3 sq.units g) 16sq.cm h) 8 2 cm VII. a) 14cm 2 b) 18cm 2 c) 54cm d) 9.6cm, 8cm VIII. a) 18cm 2 b) 7.5cm 2 c) 48cm 2 d) 26cm 2 e) 21.6cm 2 f) 120cm 2 Page 5 of 5